Click on Private Messages. Next to the list of private messages... on the right ... are check boxes. Select them, then go down to 'move to' and move to delete, then GO.
Correct, after selecting the checkboxes for the ones you wish to delete (and you have to do this both for your inbox received and outbox sent messages). Use the delete option from the "selected messages" dropdown menu. It will look similar to this:
2011 Flagstaff 831 RLBSS
I've reported my DNA missing just in case it's found somewhere bad.